Expression of type ExprTuple

from the theory of proveit.logic.sets.enumeration

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, Lambda, P, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, Set

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a_1_to_n], Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), condition = Pk_a1_to_an)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left[\forall_{P~|~P\left(a_{1}\right), P\left(a_{2}\right), \ldots, P\left(a_{n}\right)}~\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\right]\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 28 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 23 body: 6
5	ExprTuple	23
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14
13	Lambda	parameter: 25 body: 15
14	ExprRange	lambda_map: 16 start_index: 31 end_index: 32
15	Conditional	value: 17 condition: 18
16	Lambda	parameter: 36 body: 19
17	Operation	operator: 23 operand: 25
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operand: 33
20	ExprTuple	25
21	Literal
22	ExprTuple	25, 26
23	Variable
24	ExprTuple	33
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29
29	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
30	Lambda	parameter: 36 body: 33
31	Literal
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable